Matrix decomposition refers to the transformation of a given matrix into a canonical form. The decomposition process is also known as matrix factorization. Matrix decomposition is utilized in many applications to solve linear algebraic systems. Several decomposition methods, such as QR decomposition, factorize a matrix into arbitrary Q and R matrices. Cholesky decomposition is a particularly efficient method for decomposing matrices that are symmetric and have positive eigenvalues. When these conditions are true, the matrix will decompose into two triangular matrices that are the Hermitian transpose of one another. Instead of determining lower and upper triangular factors Q and R, Cholesky decomposition constructs a lower triangular matrix L whose Hermitian transpose LH can itself serve as the upper triangular part. Cholesky decomposition is utilized in a number of communication and signal processing applications including, but not limited to, linear least square computation, non-linear optimization, Monte Carlo simulation, Kalman filtration, etc.
The disclosed embodiments address one or more issues arising from matrix decomposition.